Abstract. It is well known that the concept of a triple system (= vector space equipped with a triple product < xyz >) plays an important role in the construction of simple Lie algebras or superalgebras by means of the standard embedding associated with triple systems. In this paper, we will give a standard embedding construction of Lie superalgebra of types of P(n),Q(n) and B(m,n), D(m,n) from triple systems as well as G(3),F(4) and D(2.1,α). Also, we will consider a Peirce decomposition of (-1,-1) -Freudenthal-Kantor triple systems.

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